THE DIRECTED UNIFORM HAMILTON-WATERLOO PROBLEM INVOLVING EVEN CYCLE SIZES

Abstract

In this paper, factorizations of the complete symmetric digraph K v & lowast; into uniform factors consisting of directed even cycle factors are studied as a generalization of the undirected Hamilton -Waterloo Problem. It is shown, with a few possible exceptions, that K v & lowast; can be factorized into two nonisomorphic factors, where these factors are uniform factors of K v & lowast; involving K 2 & lowast; or directed m -cycles, and directed m -cycles or 2m m -cycles for even m .